Math, asked by akilap79288, 11 months ago

Simplest form of (1 - cos2 A) (1 + cot? A) is​

Answers

Answered by lohitpravirpatnaik
4

Answer:1

Step-by-step explanation:

1 - cos^2A = sin^2A

1 + cot^2A = cosec^2A

(Sin^2A)(cosec^2A)

= sin^2A × 1/sin^2A = 1

Answered by ashishks1912
2

The simplest form of the given expression (1-cos^2A)(1+cosec^2A) is 1

Step-by-step explanation:

Given expression is (1-cos^2A)(1+cot^2A)

To find the simplest form of the give expression :

First simplify  the given expression from that we have as below

  • (1-cos^2A)(1+cot^2A)
  • =(sin^2A)(cosec^2A)   ( by using the identities (1-cos^2A)=sin^2A and (1+cot^2A)=cosec^2A )
  • =sin^2A\times (\frac{1}{sin^2A}) ( by using the identity cosec^2A=\frac{1}{sin^2A} )
  • =\frac{sin^2A}{sin^2A}
  • =1 ( simplifing the terms )
  • Therefore we get (1-cos^2A)(1+cosec^2A)=1

The simplest form of the given expression (1-cos^2A)(1+cosec^2A) is 1

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